Wave redirection, localization, and non-reciprocity in a dissipative nonlinear lattice by macroscopic Landau–Zener tunneling: Theoretical results

Abstract

We consider an asymmetric dissipative network of two semi-infinite nonlinear lattices with weak linear inter-lattice coupling and study its capacity for passive wave redirection and non-reciprocity. Each lattice is composed of linearly grounded oscillators with essentially nonlinear (i.e., non-linearizable) next-neighbor intra-lattice coupling, and it supports breather propagation. Irreversible breather redirection between lattices is governed by a macroscopic analog of the quantum Landau–Zener tunneling (LZT) effect, whereby impulsive energy initially induced to the “excited lattice” is passively and irreversibly redirected to the “absorbing lattice.” Moreover, this wave redirection is realized only in a specific range of impulse intensity (energy), otherwise motion localization occurs. In this work, we show that LZT breather redirection in the dissipative network occurs only when the normalized linear inter-coupling stiffness is larger than the viscous damping ratio of the individual lattice oscillators, with breather arrest and localization occurring otherwise. Then, through a reduced-order model, we provide guidance for selecting the system parameters of the lattice network for robust breather redirection despite the presence of dissipation. To this end, we study the acoustic non-reciprocity and formulate a quantitative measure for studying it based on measured time-series responses at the four free boundaries of the finite network. Then, we show the dependence of non-reciprocity in this system on the intensity (energy) of the applied impulse. These results pave the way for conceiving practical nonlinear lattice networks with inherent capacities for passive wave redirection and acoustic non-reciprocity that are tunable (self-adaptive) to the applied impulsive excitations.